Quadratic Function

By Manya and Eliza

Example: x -6x+5=0

a=1 b=-6 c=5

Step 1: Factor the function

(x-1) (x-5)=0

x=1 x=5

Step 2: Find the axis of symmetry:

Method 1: x+x = 1+5 = 6 =3

2 2 2
Axis=3

Method 2: -b = -(-6) =6 = 3
2a 2(1) 2

Axis=3



Step 3: Find the vertex

Method 1: Substitute axis x in the function

x²-6x=5=0
(3)²-6(3)+5+y=-4

Vertex= (3, -4)

Method 2: Find the perfect square

x²-6x+5=0
Formula x²+bx+b²

(x²-6x+9)+5-9+=0
(x-3)²-4=0

Convert it into this form: y= a (x-h)²+k
x=h
y=k

Vertex:=(x,y)=(h,k)
y=a(x-h)+k
y=1 (x-3)²+(-4)

Vertex: (3,-4)

Step 4: Find the y intercept
ax²+bx+c=0
C=y intercept

x²-6x+5=0
y intercept=5

Step 5: Find the Zeros
a(x-h)²+k=y
(x-3)²4=y
(x-3)²=4
x-3=+-√4
x-3=+-2
_
x=2+3=5
x=2-3=1